Effect of medium dependent binding energies on inferring the temperatures and freeze-out density of disassembling hot nuclear matter from cluster yields

The decay of highly excited nuclear matter produced in heavy ion collisions is a complex dynamic process, which needs, in principle, a sophisticated treatment. One simple approach is the freezeout concept in which the hot and dense matter in the initial stage is assumed to reach thermal equilibrium as long as reaction rates are high. With decreasing density, the reaction rates decrease and the equilibration process becomes suppressed. At that time the nuclear thermal and chemical equilibrium is frozen out. Often the description of the nuclear matter, in particular the distribution of clusters, is calculated within a statistical multifragmentation model assuming nuclear statistical equilibrium (NSE). Under the simplifying assumption that the final reaction product distribution is identical to the cluster distribution at the freeze out point, the thermodynamic parameters such as temperature T and particle number densities, nn and np for neutrons and protons, respectively, can be reconstructed from the observed abundances. A simple method for extracting the temperature of the fragmenting hot system was given by Albergo, Costa, Costanzo and Rubbino (ACCR) [1]. The method is based on selecting double isotope (or isotone) ratios, R2, such that the nucleon chemical potentials are eliminated leading to a relation between R2, T and the binding energies of the isotopes (isotones). This method has been used in the analysis of a large number of experiments [2]. We point out [2] that the ACCR method was modified to account for: (i) the screening due to the Coulomb interactions among fragments in the freeze-out volume by using the Wigner-Seitz approximation; (ii) the effect of radial collective flow, and (iii) the effects of post emission decay (secondary decay) processes of particles and, in particular, γ which modify the freeze-out yield ratios. Without these corrections, different double ratios R2 associated with selected sets of fragments (different thermometers) may result in significantly different temperature T (see a review in Ref. [2]). If the freeze-out density is not very low the NSE will be modified by medium effects. In this work [3] we explore the abundance of light clusters in nuclear matter at subsaturation density. With increasing density, binding energies and wave functions are modified due to medium effects. The method of ACCR for determining the temperature and free nucleon density of disassembling hot nuclear source from fragment yields is modified to include, in addition to Coulomb effects and flow, also effects of medium modifications of cluster properties, which become of importance when the nuclear matter density is above 10 fm. Recent progress in the description of clusters in low density nuclear matter [4] enables us to evaluate the abundance of deuterons, tritons and helium nuclei in a microscopic approach, taking the influence of the medium into account. Within a quantum statistical approach to the many-particle system, we determine the single-particle spectral function, which allows calculation of the density of the nucleons as a function of the temperature and the proton’s and the neutron’s chemical potentials (T, μp, μn). The main ingredient is the self-energy Σ(1,z), which is treated in different approximations. The single-particle